This paper presents a simplified Adomian method for establishing the exact receptance function of a cracked nonuniform axially functionally graded (AFG) beam carrying concentrated masses. In previous studies, the receptance functions of a beam with varying ratios of properties along the length of beam have been derived in the form of power series by using Adomian method. However, this method often requires applying the Cauchy products of infinite series, which is time consuming. The more properties of the beam, such as elastic modulus, mass density, height, or width, vary along its length, the more Cauchy products of infinite series must be computed. This study introduces a new technique to avoid calculating Cauchy products. Moreover, the proposed method requires calculating only second-order determinant for beam with an arbitrary number of cracks, resulting in further reduction of computational time compared to previous methods, which require calculating determinants of much higher order. The proposed method always provides the explicit solution for the receptance function when the elastic modulus E and moment of inertia I are expressed as polynomials of arbitrary degree. When there are cracks, the receptance function is distorted locally at crack positions. The influence of the concentrated masses on these distortions in the receptance function is investigated. Numerical simulations show that concentrated masses located at suitable positions can significantly amplify the effects of the cracks on the receptance function, which may be useful for crack detection.
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